The following is the beginning of a dialogue in my textbook. The scenario is that a student, Susan, has gone to her professor's office to discuss her (Susan's) class schedule.

This is the first line she says in the dialogue:
先生、ちょっとご相談したいことがあるんですが、今よろしいでしょうか。

I have confidence that I have a good grasp on the core meaning of the [~ことがある] pattern, when it means "It sometimes happens that . . .", "There are times when . . .", etc., as in, say,
私はよく色々な日本語の文法の点が分からないことがあります。
私は時々仕事へ行く気がすることがあります。

I *do* read the original dialog sentence, [ 先生、ちょっとご相談したいことがあるんですが、今よろしいでしょうか ], literally, as something close to "Professor, there are times when I have been wanting to consult with you [regarding my classes]. Is now a good time?”

More naturally, I think that could be read as "Professor, I have been wanting to consult with you [regarding my classes.] Is now a good time?" Is this one a reasonable reading?

What it all boils down to, ultimately, is "Why is ～ことがある is used the way it is in [ 先生、ちょっとご相談したいことがあるんですが、今よろしいでしょうか ]?

In your question, ～ことがある seems relatively easy to me.
Let’s take the phrase apart. It consists of こと, が, ある, right? Here, the phrase means literally, (there is) thing, is, existing. More naturally, it means “something is here” or “something I have”, ok?
ちょっとご相談したいことがあるんですが
“A little / I want to talk about / something I have”
would be the literal translation.
Which means, “Professor, I have something I want to talk with you”.
Then, you go on saying, “Do you have some time?”
In your example sentence, こと has nothing to do with time. It means “something” “some subject” or “some issue”.
Makes sense?

NileCat wrote:In your question, ～ことがある seems relatively easy to me.
Let’s take the phrase apart. It consists of こと, が, ある, right? Here, the phrase means literally, (there is) thing, is, existing. More naturally, it means “something is here” or “something I have”, ok?
ちょっとご相談したいことがあるんですが
“A little / I want to talk about / something I have”
would be the literal translation.
Which means, “Professor, I have something I want to talk with you”.
Then, you go on saying, “Do you have some time?”
In your example sentence, こと has nothing to do with time. It means “something” “some subject” or “some issue”.
Makes sense?

First of all, thank you for your response.

I do understand your answer. Honestly, I do. Until you showed me how I erred, I had misunderstood the Japanese sentence pattern in Susan's sentence.

So, in contrast, then, how would Susan say 'Professor, sometimes I want to have a consultation with you?’